Frequency-hopping is a method of transmitting radio signals where the carrier wave is sequentially switched among many frequency channels, using a sequence known to both transmitter and receiver. Generally speaking, an eavesdropper is only able to intercept the transmission if the sequence is known. An advantage of spread spectrum frequency hopping is that such transmissions can share a frequency band with many types of conventional transmissions with minimal interference. The spread-spectrum signals add minimal noise to the narrow-frequency communications, and vice versa; resulting in more efficient bandwidth utilization. Since they do not raise the noise floor appreciably, they are difficult to detect by an uninformed adversary. Another advantage of spread-spectrum signals is that they are highly resistant to deliberate jamming, unless the jammer knows the characteristics of the spreading. Military radios use cryptographic techniques to generate the channel sequence under the control of a secret key that the sender and receiver share.
The capability to track a frequency-hopped signal without knowledge of its hopping pattern is useful in intelligence operations. The problem is of interest in military communications, where, in addition to frequency, hop timing can also be randomly shifted to guard against unauthorized reception and jamming. Tracking the time-varying parameters (frequency, complex amplitude) of a complex sinusoid is an important problem that arises in numerous applications. In many cases the parameters can be assumed to vary slowly in time; in frequency hopping (FH) communications, however, the carrier frequency is intentionally hopped in a (pseudo-) random and discontinuous fashion. In military communications, frequency hopping (FH) is used to guard against unauthorized reception and jamming, and hop timing can also be randomized for added protection. In civilian communications (e.g., Bluetooth), FH is used to avoid persistent interference and enable uncoordinated coexistence with other systems.
Several researchers have considered the problem of tracking a frequency hopping (FH) signal without knowledge of the hopping pattern, including L. Aydin and A. Polydoros, “Hop-timing Estimation for FH Signals Using a Coarsely Channelized Receiver,” IEEE Trans. Communications, vol. 44, no. 4, pp. 516-526, April 1996 (hereinafter Aydin 1996; hereby incorporated by reference); S. Barbarossa and A. Scaglione, “Parameter Estimation of Spread Spectrum Frequency-hopping Signals Using Time-frequency Distributions,” in Proc. IEEE Int. Workshop Signal Proc. Advances in Wireless Communications (SPAWC '97), pp. 213-216, (April 1997) (hereinafter Barbarossa 1997; hereby incorporated by reference), X. Liu, N. D. Sidiropoulos, and A. Swami, “Blind High Resolution Localization and Tracking of Multiple Frequency Hopped Signals,” IEEE Trans. Signal Processing, vol. 50, no. 4, pp. 889-901, (April 2002) (hereinafter Liu 2002, hereby incorporated by reference), X. Liu, N. D. Sidiropoulos, and A. Swami, “Joint Hop Timing and Frequency Estimation for Collision Resolution in Frequency Hopped Networks,” IEEE Trans. Wireless Communications, vol. 4, no. 6, pp. 3063-3074, (November 2005) (hereinafter Liu 2005; hereby incorporated by reference), M. K. Simon, U. Cheng, L. Aydin, A. Polydoros, and B. K. Levitt, “Hop Timing Estimation for Noncoherent Frequency-hopped M-FSK Intercept Receivers,” IEEE Trans. Communications, vol. 43, no. 2/3/4, pp. 1144-1154, (February/March/April 1995) (hereinafter Simon 1995; hereby incorporated by reference). Non-parametric methods based on the spectrogram in Aydin 1996 and Simon 1995 are simple and useful as exploratory tools, but suffer from limited resolution due to leakage. It is possible to employ time-frequency distributions that are better-adapted to frequency hopping as disclosed in Barbarossa 1997, but the results are still not very satisfactory. Parametric methods for frequency hopping explicitly model the frequency as piecewise-constant, assume a “budget” on the number of hops within a given observation interval, and employ Dynamic Programming (DP) to track the sought frequency and complex amplitude parameters (as described further in Liu 2002 and Liu 2005). Other than an upper bound on the number of hops, the methods in Liu 2002 and Liu 2005 do not assume anything else about the frequencies or complex amplitudes, which are treated as deterministic unknowns. The algorithms in Aydin 1996, Liu 2002, Liu 2005, and Simon 1995 are also applicable when hop timing is random. The approaches in Liu 2002, Liu 2005 are not suitable for on-line implementation: their complexity is roughly fourth-order polynomial in the number of temporal samples, and dynamic programming requires back-tracking—implying that only short data records can be processed, and in batch mode. The approaches in Aydin 1996 and Simon 1995 are based on the use of coarse channelization—which is a useful approach for initial exploration; however it suffers from significant limitations in terms of time-frequency localization (the so-called Fourier uncertainty principle). In practice this means that the dwell frequencies are not accurately estimated and hops are often missed.
By way of background, particle filtering (PF) is an important estimation methodology that is applicable to general stochastic non-linear and/or non-Gaussian state-space models. Particle filters, also known as sequential Monte Carlo methods (SMC), are sophisticated signal and model estimation techniques based on simulation.
It is noted that particle filtering solutions for tracking slowly varying parameters of a harmonic or chirp signal are discussed in E. Tsakonas, N. D. Sidiropoulos, A. Swami, “Time-Frequency Analysis Using Particle Filtering: Closed-form Optimal Importance Function and Sampling Procedure for a Single Time-varying Harmonic,” IEEE Explore Digital Library, Nonlinear Statistical Signal Processing Workshop, 13-15 Sep. (2006) (hereinafter Tsakonas 2006; hereby incorporated by reference), and E. Tsakonas, N. D. Sidiropoulos, A. Swami, “Optimal Particle Filters for Tracking a Time-Varying Harmonic or Chirp Signal,” IEEE Trans. Signal Processing, vol. 56, no. 10, pp. 4598-4610, (October 2008) (hereinafter Tsakonas 2008; hereby incorporated by reference). Interestingly, the case of slowly varying parameters is much different, and in a sense more difficult. In particular, the divergence phenomenon encountered in Tsakonas 2006 and Tsakonas 2008 is not present in the case of frequency hopping (FH).
U.S. Pat. No. 7,035,311, hereby incorporated by reference, discloses a signal intercept and analysis processor for a wideband intercept receiver system including at least one wideband receiver with a signal detector operatively connectable to the wideband receiver and a signal extractor operatively connected to the signal detector and connectable to the wideband receiver for performing signal extraction directly on a wideband signal output of the receiver and for performing the signal extraction only upon detection of a signal by the signal detector. The signal detector includes a generator of a coarsely sampled or decimated time-frequency representation of the wideband signal output. The time-frequency representation is decimated or coarsely sampled in time compared to an inverse frequency filter bandwidth used in the time-frequency representation. The generator preferably includes a digital filter bank. The digital filter bank in turn may include means for performing a sequence of windowed FFTs on samples of the wideband signal output, wherein a stride between consecutive one of the FFTs is considerably larger than a length of each of the FFTs.
U.S. Pat. No. 5,239,555, hereby incorporated by reference, discloses a frequency hopping interceptor for determining bandwidth, hop number, dwell time, hop channel spacing and hop frequencies. A compressive receiver, having a passband greater than the bandwidth, samples received signals at a scan rate greater than the hop rate. On each scan, the receiver separates the received signal into its frequency components. A histogram memory, connected to the receiver, stores a frequency distribution of the frequency components including the scan periods. A data processor uses the histogram memory to determine the FH parameters.